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To ensure the high level of automation required in today's industrial applications, next-generation wireless networks must enable real-time control and automation of dynamic processes with the requirements of extreme low-latency and ultra-reliable communications. In this paper, we provide a performance assessment for the co-existence of a public enhanced mobile broadband (eMBB) and a local non-public factory (URLLC) network and evaluate the network conditions under which the stringent latency and reliability requirements of factory automation applications are met. The evaluations consider both an unsynchronized and a synchronized time division duplexing (TDD) deployment between the networks, as well as scenarios both with and without any macro eMBB traffic located inside the factory. The results show that an unsynchronized deployment is possible if the isolation between the networks is sufficiently high, either as a result of a separation distance, wall loss or the use of separate frequencies for the networks. A synchronized deployment will avoid the cross-link interference, but it will not resolve the problems related to the closed access and the near-far interference. If the factory contains eMBB traffic served by the overlaid macro cells, the performance of both networks will suffer due to a high level of cross-link and near-far interference. The problems related to the cross-link interference can be resolved by synchronizing the networks, while the level of the near-far interference can be reduced by allowing the eMBB users to be connected to base stations located inside the factory. Finally, if an unsynchronized deployment is desired, the factory should be deployed on an isolated frequency.